We have a silo of radius R. Somewhere on the circumference, there is a pole with a chain of radius r attached to it. The other end of the chain is keeping Spot the dog from running around randomly. Spot can move around freely, until the chain becomes taught.What is the maximum area of movement Spot can cover? (Note: the chain wraps around the silo for angles greater than 90 degrees in either direction, using the pole as a reference point, which effectively reduces the length of the chain available for Spot to move. The reference point of the arc that spot traces out also seems to move along the circumference of the silo for angles greater than 90 degrees in either direction).
It looks possible, but is a bit of a hefty solution. Needs approaching using polar coordinates. It's possible to find the area covered, but can't accurately calculate the boundary of that area, due to the expressions involved. Can try to type out a full solution, watch this space...
